Survey on Reversible Watermarking Techniques of Echocardiography

In critical domains such as medical and military, reversible watermarking (RW) has been used. In the medical domain, different modalities are used to store patient information. The current study focuses on the application of RW in echocardiography data. Mostly, RW is applied to protect patient data without affecting the quality of the decoded image. The RW methods are benchmarked as per imperceptibility, robustness, and payload. The survey presents a comparison of state-of-the-art RW techniques. The imperceptibility and payload are balanced through a tradeoff. It has been observed in the literature that most of the RW methods lack robustness, and very small-scale robustness has been achieved in this domain of watermarking. Different types of RW, i.e., fragile, semifragile, and robust methods, are being compared and reviewed. Mostly, fragile methods are developed on the error-expansion techniques built on histogram shifting-based approach. In this study, several RW methods are compared and the results are presented.

Extended Error Expansion of Classical Midpoint Rectangle Rule for Cauchy Principal Value Integrals on an Interval

The classical composite midpoint rectangle rule for computing Cauchy principal value integrals on an interval is studied. By using a piecewise constant interpolant to approximate the density function, an extended error expansion and its corresponding superconvergence results are obtained. The superconvergence phenomenon shows that the convergence rate of the midpoint rectangle rule is higher than that of the general Riemann integral when the singular point coincides with some priori known points. Finally, several numerical examples are presented to demonstrate the accuracy and effectiveness of the theoretical analysis. This research is meaningful to improve the accuracy of the collocation method for singular integrals.